Franco Vazquez's goal after nine minutes did the damage as the Rossoblu bow out of Italy's top-flight after a 10-year stay.
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However, dropped points were not an option on an afternoon which began with Paul-Jose M'Poku firing agonisingly wide after five minutes.
Diego Farias's blocked piledriver raised pulses among the away fans shortly after, yet the visiting supporters went from nervous to jubilant within minutes as Vazquez fired Palermo ahead.
Sorrentino reproduced those heroics with a fine save to keep out Farias before the break in what proved Cagliari's last clear-cut opportunity.
On 74 minutes, Robin Quaison could have confirmed Cagliari's relegation, but miss did not prove costly as Palermo condemned their opponents to Serie B next season.